
We computed the entropy as follows [1]}, [2]}
\(S=&\dfrac{\mathcal {A}}{4}f_{R}=\dfrac{\mathcal {A}}{4}\left[1-\dfrac{2\alpha }{r^2} \left(h^{\prime \prime }r^2+4r h^{\prime }-2+2h\right)\right]_{r=r_{+}}=\pi r_{+}^{2}\left[1-\dfrac{2\alpha }{r_{+}^2} \left(h_{2}r_{+}^2+4r_{+}h_{1}-2\right)\right].\) 
